Closed-form pricing formula for foreign equity option with credit risk

Donghyun Kim,Ji-Hun Yoon,Geonwoo Kim

doi:10.1186/s13662-021-03486-7

Donghyun Kim, Ji-Hun Yoon + Show 1 more

Open Access

https://doi.org/10.1186/s13662-021-03486-7

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Abstract

Since credit risk in the over-the-counter (OTC) market has undoubtedly become very important issue, credit risk has to be considered when the options in the OTC market are priced. In this paper, we consider the valuation of foreign equity options with credit risk. In order to derive a closed-form pricing formula of this option, we adopt the partial differential equation (PDE) approach and use the Mellin transform method to solve the PDE. Specifically, triple Mellin transforms are used, and the pricing formula is presented as 3-dimensional normal cumulative distribution functions. Finally, we verify that our closed-form formula is accurate by comparing it with the numerical result from the Monte-Carlo simulation.

Highlights

Since the financial crisis in 2008, credit risk has been definitely the most important issue for researchers and practitioners in the financial market
This paper deals with the valuation of foreign equity option price with credit risk based on the partial differential equation (PDE) approach and provides a closed-form pricing formula of the options using the Mellin transforms
4 Concluding remarks Foreign equity options belong to the popular exotic options in the over-the-counter markets, and credit risk is an important issue in the OTC market

Summary

Introduction

Since the financial crisis in 2008, credit risk has been definitely the most important issue for researchers and practitioners in the financial market. We derive a closed-form solution of foreign equity option price with credit risk based on the partial differential equation (PDE) approach. We use the Mellin transforms to solve the PDE for the price of foreign equity options with credit risk. This paper deals with the valuation of foreign equity option price with credit risk based on the PDE approach and provides a closed-form pricing formula of the options using the Mellin transforms.

The terminal condition is expressed as

Number of simulations